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Description

Multi-body Kinematics and Dynamics with Lie Groups explores the use of Lie groups in the kinematics and dynamics of rigid body systems.

The first chapter reveals the formal properties of Lie groups on the examples of rotation and Euclidean displacement groups. Chapters 2 and 3 show the specific algebraic properties of the displacement group, explaining why dual numbers play a role in kinematics (in the so-called screw theory). Chapters 4 to 7 make use of those mathematical tools to expound the kinematics of rigid body systems and in particular the kinematics of open and closed kinematical chains. A complete classification of their singularities demonstrates the efficiency of the method.

Dynamics of multibody systems leads to very big computations. Chapter 8 shows how Lie groups make it possible to put them in the most compact possible form, useful for the design of software, and expands the example of tree-structured systems.

This book is accessible to all interested readers as no previous knowledge of the general theory is required.

Key Features

Presents a overview of the practical aspects of Lie groups based on the example of rotation groups and the Euclidean group

Makes it clear that the interface between Lie groups methods in mechanics and numerical calculations is very easy

Includes theoretical results that have appeared in scientific articles

Readership

Engineers and Scientists working with multibody systems (robotics, designers). Organizations such as ASME, ASCE, any university libraries

Table of Contents

1. The Displacement Group as a Lie Group2. Dual Numbers and "Dual Vectors" in Kinematics3. The "Transference Principle"4. Kinematics of a Rigid Body and Rigid Body Systems5. Kinematics of Open Chains, Singularities6. Closed Kinematic Chains: Mechanisms Theory7. Dynamics8. Dynamics of Rigid Body Systems